In particular in the case of LED incandescent lamp retrofit lamps which are provided to replace conventional incandescent lamps and use light-emitting diodes as light sources, it is desirable that emission of light occurs into the greatest possible spatial angle range. Diffusers are normally used for this purpose. However, the diffusers permit beam widening only over a limited angle and, in addition, some of the light radiated into the diffusers is lost since, for example, it is reflected back at the inner side of the diffuser and to some extent is reabsorbed by the surfaces or the LEDs themselves, and the light emitted by the illumination device loses brilliance.